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Math Expert V
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What is the area of triangle ABC above? (1) DBC is an equilateral tri  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 60% (01:58) correct 40% (01:56) wrong based on 57 sessions

HideShow timer Statistics  What is the area of triangle ABC above?

(1) DBC is an equilateral triangle.
(2) ABD is an isosceles triangle.

Attachment: #GREpracticequestion Which of the following statements individually provide(s).jpg [ 9.8 KiB | Viewed 553 times ]

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What is the area of triangle ABC above? (1) DBC is an equilateral tri  [#permalink]

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Bunuel wrote: What is the area of triangle ABC above?

(1) DBC is an equilateral triangle.
(2) ABD is an isosceles triangle.

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#GREpracticequestion Which of the following statements individually provide(s).jpg

#1
DBC is equilaterlal so angle BDC =BCD=CDB= 60 each and angle BDA=120 and ABD=30 as given ABC is 90*
so BAD=ABD=30 ∆ABD isosceles ∆ ; using the x:x:x√2 rule ; side BD & AD = 5√6
so area ; 1/2 * 5*√6 * 10√6 = 25*6 ; 150
#2
isosceles ∆ given so using x:x:x√2 rule ; side BD & AD = 5√6
but no info about DC & BC insufficient
IMO A
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Originally posted by Archit3110 on 23 May 2019, 09:28.
Last edited by Archit3110 on 24 May 2019, 00:01, edited 1 time in total.
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Re: What is the area of triangle ABC above? (1) DBC is an equilateral tri  [#permalink]

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Stat1)
If tr DBC is eq it means angle c is 60,so angle A is 30.
Now we can find area of abc
Stat2)
If abc is isoceles it means angle a and c are both 45.
Now we can find area.

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What is the area of triangle ABC above? (1) DBC is an equilateral tri  [#permalink]

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deshwalankit04 wrote:
Stat1)
If tr DBC is eq it means angle c is 60,so angle A is 30.
Now we can find area of abc
Stat2)
If abc is isoceles it means angle a and c are both 45.
Now we can find area.

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deshwalankit04 see highlighted part ; how and why ? can you please explain in detail
also ABD is an isosceles triangle not what you have mentioned..
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Re: What is the area of triangle ABC above? (1) DBC is an equilateral tri  [#permalink]

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1)B is shown as 90 degrees in ABC and in DBC all will be 60 degrees as it is equlateral;Now we know in ABC ,B is 90 and C is 60 so A is 30.

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Re: What is the area of triangle ABC above? (1) DBC is an equilateral tri  [#permalink]

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Because from statement 1 we know the breakup of the BDC thus ABC is a 90-60-30 triangle
Statement 2 insufficient we just know ABD is isoceles we Do not know the breakup of any angle

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Re: What is the area of triangle ABC above? (1) DBC is an equilateral tri  [#permalink]

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This is a moderately difficult question on Geometry, specifically on properties of triangles in general and right angled triangles in particular.

ABC is a right angled triangle, right angled at B. The area of triangle ABC = ½ * AB * BC.
AB = 10√3, so, any data that can help us calculate BC will be sufficient data.

Using Statement I alone, since triangle DBC is an equilateral triangle, angle BCA = 60 degrees. Therefore, in triangle ABC, angle BAC = 30 degrees. So, triangle ABC is a 30-60-90 right triangle.

In a 30-60-90 right triangle, if the side opposite to the 30 degree angle is ‘x’, then the side opposite to the 60 degree angle will be ‘x√3’ and the hypotenuse will be ‘2x’.

In triangle ABC, side AB is opposite 60 degrees. Hence, the side opposite to 30 degrees, BC has to be 10. This is sufficient data to calculate a unique value of the area of the triangle. So, the possible answers are A or D. Options B, C and E can be ruled out.

Using statement II alone, we know that triangle ABD is an isosceles triangle. However we do not know which sides of ABD are equal. Also, even if we know the lengths of the sides, we need data about the angles, to be able to calculate the length of BC. So, statement II alone is insufficient and hence option D can be eliminated.
The correct answer option is A.

If you are conversant with the basic properties of triangles and also specific details like properties of a 30-60-90 triangle, this question should not take you more than a minute and a half to solve. The second statement, though, should be interpreted with care. When it comes to DS questions on Geometry, always remember that unless you get a UNIQUE figure from the data given, the data cannot be considered as sufficient. And in our case, statement II will not give us a unique figure.

Hope this helps!
_________________ Re: What is the area of triangle ABC above? (1) DBC is an equilateral tri   [#permalink] 28 May 2019, 20:52
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